Introduction to systems of equations
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Just in case we encounter any more trolls who want us to figure out what types of money they have in their pockets, we have devised an exercise for you to practice with. And this is to solve systems of equations visually. So they say right over here, graph this system of equations and solve. And they give us two equations. This first one in blue, y is equal to 7/5x minus 5, and then this one in green, y is equal to 3/5x minus 1. So let's graph each of these, and we'll do it in the corresponding color. So first let's graph this first equation. So the first thing I see is its y-intercept is negative 5. Or another way to think about it, when x is equal to 0, y is going to be negative 5. So let's try this out. So when x is equal to 0, y is going to be equal to negative 5. So that makes sense. And then we see its slope is 7/5. This was conveniently placed in slope-intercept form for us. So it's rise over run. So for every time it moves 5 to the right it's, going to move seven up. So if it moves 1, 2, 3, 4, 5 to the right, it's going to move 7 up. 1, 2, 3, 4, 5, 6, 7. So it'll get right over there. Another way you could have done it is you could have just tested out some values. You could have said, oh, when x is equal to 0, y is equal to negative 5. When x is equal to 5, 7/5 times 5 is 7 minus 5 is 2. So I think we've properly graphed this top one. Let's try this bottom one right over here. So we have when x is equal to 0, y is equal to negative 1. So when x is equal to 0, y is equal to negative 1. And the slope is 3/5. So if we move over 5 to the right, we will move up 3. So we will go right over there, and it looks like they intersect right at that point, right at the point x is equal to 5, y is equal to 2. So we'll type in x is equal to 5, y is equal to 2. And you could even verify by substituting those values into both equations, to show that it does satisfy both constraints. So let's check our answer. And it worked.